Oh, this is amusing.
Even assuming you got Cullen mad enough to actually fight with the intent of killing a human, he'd rely mainly on his super strength, speed, supposed invulnerability, and mind reading. He's a four-trick pony. The rest of his brain is devoted to stalking Bella.
Fullmetal, however, is inventive. Sparkleboy, while vampiric, is made of the same base components as a human, i.e. lots of carbon. After working out the "invulnerability" bit, I think our Ed will make the connection and start using the trick he used on Greed. While landing hits on a mind-reader would be difficult, I think he'd still be able to do it; he'd be able to use physics and terrain to his advantage (even if you can tell that I'm going to make this massive hole under your feet, you can't dodge gravity, now can you?) After Fullmetal landed one good hit using carbon deconstruction, there would just be a bunch of sparkly pieces everywhere, which he could then easily turn into something that can't regenerate.
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